Theory and Algorithms Commons^™

Quantum Machine Learning Models: Principles, Frameworks, And Computational Challenges, K. A. Jayabalaji, S. Venkata Anand, Dineshkumar Rajendran, Prasanta Chatterjee Biswas, Sardor Omonov, Rubaid Ashfaq

Computer Science Faculty Publications

Quantum machine learning (QML) has become an optimistic avenue of harnessing quantum computation in data-driven modeling, especially of issues with high dimensionality and complicated correlations. Current methods are generally based on fixed or over-parameterized quantum circuits, and hence restricted to scalability as well as unproductive optimization in real-world hardware. This chapter introduces a hybrid quantum-classical learning system that is adaptive and provides principled quantum data encoding, architecture-conscious variational circuit design and resource-optimal optimization. The technique is based on the concepts of quantum architecture search and subspace-preserving transformations to trade expressiveness with trainability, and discretize the quantum model into a classical …

Pure And Strong Nash Equilibrium Computation In Compactly Representable Aggregate Games, Jared Soundy, Mohammad T. Irfan, Hau Chan

Research & Publications

Aggregate games model interdependent decision making when an agent’s utility depends on their own choice and the aggregation of everyone's choices. We define a compactly representable subclass of aggregate games we call additive aggregate games, which encompasses popular games like congestion games, anonymous games, Schelling games, etc. We study computational questions on pure Nash equilibrium (PNE) and pure strong Nash equilibrium (SNE). We show that PNE existence is NP-complete for very simple cases of additive aggregate games. We devise an efficient algorithmic scheme for deciding the existence of a PNE and computing one (if it exists) for bounded aggregate space. …

The Primitive Root Problem: A Problem In Bqp, Shixin Wu

Mathematical Sciences Technical Reports (MSTR)

Shor’s algorithm proves that the discrete logarithm problem is in BQP. Based on his algorithm, we prove that the primitive root problem, a problem that verifies if some integer g is a primitive root modulo p where p is the largest prime number smaller than 2n for a given n, which is assumed to be harder than the discrete logarithm problem, is in BQP by using an oracle quantum Turing machine.

Parameter Estimation And Inference Of Spatial Autoregressive Model By Stochastic Gradient Descent, Gan Luan

Dissertations

Stochastic gradient descent (SGD) is a popular iterative method for model parameter estimation in large-scale data and online learning settings since it goes through the data in only one pass. While SGD has been well studied for independent data, its application to spatially-correlated data largely remains unexplored. This dissertation develops SGD-based parameter estimation and statistical inference algorithms for the spatial autoregressive (SAR) model, a common model for spatial lattice data.

This research contains three parts. (I) The first part concerns SGD estimation and inference for the SAR mean regression model. A new SGD algorithm based on maximum likelihood estimator (MLE) …

Sparsity And Weak Supervision In Quantum Machine Learning, Seyran Saeedi

Theses and Dissertations

Quantum computing is an interdisciplinary field at the intersection of computer science, mathematics, and physics that studies information processing tasks on a quantum computer. A quantum computer is a device whose operations are governed by the laws of quantum mechanics. As building quantum computers is nearing the era of commercialization and quantum supremacy, it is essential to think of potential applications that we might benefit from. Among many applications of quantum computation, one of the emerging fields is quantum machine learning. We focus on predictive models for binary classification and variants of Support Vector Machines that we expect to be …

Powers And Behaviors Of Directed Self-Assembly, Trent Allen Rogers

Graduate Theses and Dissertations

In nature there are a variety of self-assembling systems occurring at varying scales which give rise to incredibly complex behaviors. Theoretical models of self-assembly allow us to gain insight into the fundamental nature of self-assembly independent of the specific physical implementation. In Winfree's abstract tile assembly model (aTAM), the atomic components are unit square "tiles" which have "glues" on their four sides. Beginning from a seed assembly, these tiles attach one at a time during the assembly process in an asynchronous and nondeterministic manner.

We can gain valuable insights into the nature of self-assembly by comparing different models of self-assembly …

High Dimensional Outlier Detection, Omid Khormali

Graduate Student Theses, Dissertations, & Professional Papers

In statistics and data science, outliers are data points that differ greatly from other observations in a data set. They are important attributes of the data because they can dramatically influence patterns and relationships manifested by non-outliers. It is therefore very important to detect and adequately deal with outliers. Recently, a novel algorithm, the ROMA algorithm, has been proposed [11]. In this paper, we propose a modification of the ROMA algorithm that reduces its computational complexity from $O(n^2 m)$ to $O((n/(2^m-o(1)))^2 m)$ where $n$ is the number of data points and $m$ is the dimension of the space. And as …

Algorithmic Issues In Some Disjoint Clustering Problems In Combinatorial Circuits, Zola Nailah Donovan

Graduate Theses, Dissertations, and Problem Reports (ETD)

As the modern integrated circuit continues to grow in complexity, the design of very large-scale integrated (VLSI) circuits involves massive teams employing state-of-the-art computer-aided design (CAD) tools. An old, yet significant CAD problem for VLSI circuits is physical design automation. In this problem, one needs to compute the best physical layout of millions to billions of circuit components on a tiny silicon surface. The process of mapping an electronic design to a chip involves several physical design stages, one of which is clustering. Even for combinatorial circuits, there exist several models for the clustering problem. In particular, we consider the …

Modeling, Learning And Reasoning About Preference Trees Over Combinatorial Domains, Xudong Liu

Theses and Dissertations--Computer Science

In my Ph.D. dissertation, I have studied problems arising in various aspects of preferences: preference modeling, preference learning, and preference reasoning, when preferences concern outcomes ranging over combinatorial domains. Preferences is a major research component in artificial intelligence (AI) and decision theory, and is closely related to the social choice theory considered by economists and political scientists. In my dissertation, I have exploited emerging connections between preferences in AI and social choice theory. Most of my research is on qualitative preference representations that extend and combine existing formalisms such as conditional preference nets, lexicographic preference trees, answer-set optimization programs, possibilistic …

Usefulness Of Infeasible Solutions In Evolutionary Search: An Empirical And Mathematical Study, Lyndon While, Philip Hingston

Research outputs 2013

When evolutionary algorithms are used to solve constrained optimization problems, the question arises how best to deal with infeasible solutions in the search space. A recent theoretical analysis of two simple test problems argued that allowing infeasible solutions to persist in the population can either help or hinder the search process, depending on the structure of the fitness landscape. We report new empirical and mathematical analyses that provide a different interpretation of the previous theoretical predictions: that the important effect is on the probability of finding the global optimum, rather than on the time complexity of the algorithm. We also …

Combinatorics Using Computational Methods, Derrick Stolee

Department of Mathematics: Dissertations, Theses, and Student Research

Computational combinatorics involves combining pure mathematics, algorithms, and computational resources to solve problems in pure combinatorics. This thesis provides a theoretical framework for combinatorial search, which is then applied to several problems in combinatorics. Some results in space-bounded computational complexity are also presented.

Flipping The Winner Of A Poset Game, Adam O. Kalinich '12

Student Publications & Research

Partially-ordered set games, also called poset games, are a class of two-player combinatorial games. The playing field consists of a set of elements, some of which are greater than other elements. Two players take turns removing an element and all elements greater than it, and whoever takes the last element wins. Examples of poset games include Nim and Chomp. We investigate the complexity of computing which player of a poset game has a winning strategy. We give an inductive procedure that modifies poset games to change the nim-value which informally captures the winning strategies in the game. For a generic …

Random Automata Networks: Why Playing Dice Is Not A Vice, Christof Teuscher

Systems Science Friday Noon Seminar Series

Random automata networks consist of a set of simple compute nodes interacting with each other. In this generic model, one or multiple model parameters, such as the the node interactions and/or the compute functions, are chosen at random. Random Boolean Networks (RBNs) are a particular case of discrete dynamical automata networks where both time and states are discrete. While traditional RBNs are generally credited to Stuart Kauffman (1969), who introduced them as simplified models of gene regulation, Alan Turing proposed unorganized machines as early as 1948. In this talk I will start with Alan Turing's early work on unorganized machines, …

Solving Continuous Linear Least-Squares Problems By Iterated Projection, Ralf Juengling

Computer Science Faculty Publications and Presentations

I present a new divide-and-conquer algorithm for solving continuous linear least-squares problems. The method is applicable when the column space of the linear system relating data to model parameters is “translation invariant”. The central operation is a matrix- vector product, which makes the method very easy to implement. Secondly, the structure of the computation suggests a straightforward parallel implementation.

A complexity analysis for sequential implementation shows that the method has the same asymptotic complexity as well-known algorithms for discrete linear least-squares. For illustration we work out the details for the problem of fitting quadratic bivariate polyno- mials to a piecewise …

Networks - Ii: Optimal Fractional Frequency Reuse (Ffr) And Resource Allocation In Multiuser Ofdma System, Naveed Ul Hassan, Mohamad Assaad

International Conference on Information and Communication Technologies

In this paper we determine the optimal fractional frequency reuse (FFR) and resource allocation in OFDMA system. Since the users at the cell edge are more exposed to inter-cell interference therefore each cell is partitioned into two regions; inner region and outer region. We determine the optimal FFR factor for the outer region, bandwidth assigned to each region and subcarrier and power allocation to all the users in the cell. The problem is formulated as sum-power minimization problem subject to minimum rate constraints in both the regions. This is a mixed linear integer programming problem which is relaxed into a …

Variability Analysis Of Discrete Cosine Transform Coefficient (Dctc) Features For Speech Processing, Bingjun Dai

Electrical & Computer Engineering Theses & Dissertations

In this research, the variability of Discrete Cosine Transform Coefficient (DCTC) features was investigated. Additionally, a new pitch-synchronous processing method was explored to increase the stability of features and to reduce window effects when compared to the regular method. The noise sources that lead to feature variability were analyzed, and different smoothing methods were tested. It was found that longer frames, frequency warping, time smoothing of the log spectrum, and DCS level time smoothing, all help reduce DCTC variability and increase classification performance. The pitch­ synchronous method was implemented with Matlab. Important processing methods, including pitch period estimation, time­ domain …

On The Difficulty Of Manhattan Channel Routing, Ronald I. Greenberg, Joseph Jaja, Sridhar Krishnamurthy

Computer Science: Faculty Publications and Other Works

We show that channel routing in the Manhattan model remains difficult even when all nets are single-sided. Given a set of n single-sided nets, we consider the problem of determining the minimum number of tracks required to obtain a dogleg-free routing. In addition to showing that the decision version of the problem isNP-complete, we show that there are problems requiring at least d+Omega(sqrt(n)) tracks, where d is the density. This existential lower bound does not follow from any of the known lower bounds in the literature.